Problem: Alice has a cute cat. To keep her cat fit, Alice wants to design an exercising walk for her cat! 

Initially, Alice's cat is located in a cell (x,y) of an infinite grid. According to Alice's theory, cat needs to move: 

  * exactly a steps left: from (u,v) to (u-1,v); 
  * exactly b steps right: from (u,v) to (u+1,v); 
  * exactly c steps down: from (u,v) to (u,v-1); 
  * exactly d steps up: from (u,v) to (u,v+1). 



Note that the moves can be performed in an arbitrary order. For example, if the cat has to move 1 step left, 3 steps right and 2 steps down, then the walk right, down, left, right, right, down is valid.

Alice, however, is worrying that her cat might get lost if it moves far away from her. So she hopes that her cat is always in the area [x_1,x_2]× [y_1,y_2], i.e. for every cat's position (u,v) of a walk x_1 ≤ u ≤ x_2 and y_1 ≤ v ≤ y_2 holds.

Also, note that the cat can visit the same cell multiple times.

Can you help Alice find out if there exists a walk satisfying her wishes?

Formally, the walk should contain exactly a+b+c+d unit moves (a to the left, b to the right, c to the down, d to the up). Alice can do the moves in any order. Her current position (u, v) should always satisfy the constraints: x_1 ≤ u ≤ x_2, y_1 ≤ v ≤ y_2. The staring point is (x, y).

You are required to answer t test cases independently.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^3) — the number of testcases. 

The first line of each test case contains four integers a, b, c, d (0 ≤ a,b,c,d ≤ 10^8, a+b+c+d ≥ 1).

The second line of the test case contains six integers x, y, x_1, y_1, x_2, y_2 (-10^8 ≤ x_1≤ x ≤ x_2 ≤ 10^8, -10^8 ≤ y_1 ≤ y ≤ y_2 ≤ 10^8).

Output

For each test case, output "YES" in a separate line, if there exists a walk satisfying her wishes. Otherwise, output "NO" in a separate line. 

You can print each letter in any case (upper or lower).

Example

Input


6
3 2 2 2
0 0 -2 -2 2 2
3 1 4 1
0 0 -1 -1 1 1
1 1 1 1
1 1 1 1 1 1
0 0 0 1
0 0 0 0 0 1
5 1 1 1
0 0 -100 -100 0 100
1 1 5 1
0 0 -100 -100 100 0


Output


Yes
No
No
Yes
Yes
Yes

Note

In the first test case, one valid exercising walk is $$$(0,0)→ (-1,0) → (-2,0)→ (-2,1) → (-2,2)→ (-1,2)→(0,2)→ (0,1)→ (0,0) → (-1,0)$$$

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;
import java.lang.*;
 
import static java.lang.Math.*;

public class P1 implements Runnable 
{
    public static void main(String args[]) throws Exception 
    {
        new Thread(null, new P1(),"P1",1<<27).start();
    }


    public void run()
    {
        InputReader sc = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);
        int t=sc.nextInt();
        while(t-->0){
            int a=sc.nextInt();
            int b=sc.nextInt();
            int c=sc.nextInt();
            int d=sc.nextInt();

            int x=sc.nextInt();
            int y=sc.nextInt();
            int x1=sc.nextInt();
            int y1=sc.nextInt();
            int x2=sc.nextInt();
            int y2=sc.nextInt();    
            int temp=0;
            boolean flag=false;
            if (Math.abs(x1-x)>=1 || Math.abs(x2-x)>=1) {
                    if (a>=b) {
                        temp=a-b;
                    
                        if (Math.abs(x1-x)>=temp) {}
                        else{
                                // w.println("2");
                                w.println("No");
                                // w.println("2");

                                flag=true;       
                        }        
                    }
                    else{
                        temp=b-a;
                            if (Math.abs(x2-x)>=temp) {
                            }
                            else{
                                // w.println("3");
                                w.println("No");
                                flag=true;    
                            }
                    }
                }
            else{
                        if (a==0 && b==0) {}
                        else{
                            w.println("No");
                            flag=true;   
                        }
            }

            if(!flag && ((Math.abs(y1-y)>=1) || (Math.abs(y2-y)>=1))){
               if (c>=d) {
                    temp=c-d;
                        if (Math.abs(y1-y)>=temp) {}
                        else{
                                w.println("No");
                                flag=true;       
                        }    
                }
                else{
                    temp=d-c;
                        if (Math.abs(y2-y)>=temp) {}
                        else{
                            w.println("No");
                            flag=true;    
                        }
                }
            }
            else{
                    if (!flag) {
                        if (c==0 && d==0) {}
                        else{
                            w.println("No");
                            flag=true;   
                        }   
                    }
            }
            if (!flag) {
                w.println("Yes");
            }
            System.out.flush();
        }
        w.close();
    }

    static class InputReader 
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) 
        {
            this.stream = stream;
        }
        
        public int read()
        {
            if (numChars==-1) 
                throw new InputMismatchException();
            
            if (curChar >= numChars) 
            {
                curChar = 0;
                try
                {
                    numChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                
                if(numChars <= 0)               
                    return -1;
            }
            return buf[curChar++];
        }
     
        public String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() 
        {
            int c = read();
            
            while(isSpaceChar(c)) 
                c = read();
            
            int sgn = 1;
        
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            
            int res = 0;
            do
            {
                if(c<'0'||c>'9') 
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c)); 
        
            return res * sgn;
        }
        
        public long nextLong() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            long res = 0;
            
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
                return res * sgn;
        }
        
        public double nextDouble() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') 
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
    
        public String readString() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = read();
            } 
            while (!isSpaceChar(c));
            
            return res.toString();
        }
     
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public String next()
        {
            return readString();
        }
        
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
    
    
    // if modulo is required set value accordingly
    public static long[][] matrixMultiply2dL(long t[][],long m[][])
    {
        long res[][]= new long[t.length][m[0].length];
        
        for(int i=0;i<t.length;i++)
        {
            for(int j=0;j<m[0].length;j++)
            {
                res[i][j]=0;
                for(int k=0;k<t[0].length;k++)
                {
                    res[i][j]+=t[i][k]+m[k][j];
                }
            }
        }
        
        return res;
    }
    
    static void Seive(){
        int temp=1000001;
        boolean[] flag=new boolean[temp];
        Arrays.fill(flag,true);
        flag[0]=false;
        flag[1]=false;
        for (int i=2;i<=Math.sqrt(temp);++i) {
            if (flag[i]) {
                for (int j=2;i*j<temp;++j) {
                    flag[i*j]=false;
                }
            }
        }
    }

    static long combination(long n,long r)
    {
        long ans=1;
        for(long i=0;i<r;i++)
        {
            ans=(ans*(n-i))/(i+1);
        }
        return ans;
    }

    // **just change the name of class from Main to reuquired**
    
}